LMFDB - Embedded newform 845.2.e.c.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.c.191.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 + 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.00000 q^{5} +(0.292893 - 0.507306i) q^{6} +(-0.414214 + 0.717439i) q^{7} +1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.207107 + 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.00000 q^{5} +(0.292893 - 0.507306i) q^{6} +(-0.414214 + 0.717439i) q^{7} +1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(0.292893 + 0.507306i) q^{11} -2.58579 q^{12} -0.343146 q^{14} +(0.707107 + 1.22474i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.41421 - 4.18154i) q^{17} +0.414214 q^{18} +(1.70711 - 2.95680i) q^{19} +(-0.914214 + 1.58346i) q^{20} +1.17157 q^{21} +(-0.121320 + 0.210133i) q^{22} +(0.707107 + 1.22474i) q^{23} +(-1.12132 - 1.94218i) q^{24} +1.00000 q^{25} -5.65685 q^{27} +(0.757359 + 1.31178i) q^{28} +(-2.82843 - 4.89898i) q^{29} +(-0.292893 + 0.507306i) q^{30} -10.2426 q^{31} +(2.20711 - 3.82282i) q^{32} +(0.414214 - 0.717439i) q^{33} +2.00000 q^{34} +(0.414214 - 0.717439i) q^{35} +(-0.914214 - 1.58346i) q^{36} +(4.24264 + 7.34847i) q^{37} +1.41421 q^{38} -1.58579 q^{40} +(-4.41421 - 7.64564i) q^{41} +(0.242641 + 0.420266i) q^{42} +(-1.53553 + 2.65962i) q^{43} +1.07107 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.292893 + 0.507306i) q^{46} -0.828427 q^{47} +(-2.12132 + 3.67423i) q^{48} +(3.15685 + 5.46783i) q^{49} +(0.207107 + 0.358719i) q^{50} -6.82843 q^{51} -14.4853 q^{53} +(-1.17157 - 2.02922i) q^{54} +(-0.292893 - 0.507306i) q^{55} +(-0.656854 + 1.13770i) q^{56} -4.82843 q^{57} +(1.17157 - 2.02922i) q^{58} +(5.12132 - 8.87039i) q^{59} +2.58579 q^{60} +(4.00000 - 6.92820i) q^{61} +(-2.12132 - 3.67423i) q^{62} +(0.414214 + 0.717439i) q^{63} -4.17157 q^{64} +0.343146 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-4.41421 - 7.64564i) q^{68} +(1.00000 - 1.73205i) q^{69} +0.343146 q^{70} +(-3.94975 + 6.84116i) q^{71} +(0.792893 - 1.37333i) q^{72} +8.48528 q^{73} +(-1.75736 + 3.04384i) q^{74} +(-0.707107 - 1.22474i) q^{75} +(-3.12132 - 5.40629i) q^{76} -0.485281 q^{77} +8.48528 q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.82843 - 3.16693i) q^{82} +8.82843 q^{83} +(1.07107 - 1.85514i) q^{84} +(-2.41421 + 4.18154i) q^{85} -1.27208 q^{86} +(-4.00000 + 6.92820i) q^{87} +(0.464466 + 0.804479i) q^{88} +(3.00000 + 5.19615i) q^{89} -0.414214 q^{90} +2.58579 q^{92} +(7.24264 + 12.5446i) q^{93} +(-0.171573 - 0.297173i) q^{94} +(-1.70711 + 2.95680i) q^{95} -6.24264 q^{96} +(1.82843 - 3.16693i) q^{97} +(-1.30761 + 2.26485i) q^{98} +0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} - 16 q^{12} - 24 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 16 q^{21} + 8 q^{22} + 4 q^{24} + 4 q^{25} + 20 q^{28} - 4 q^{30} - 24 q^{31} + 6 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{40} - 12 q^{41} - 16 q^{42} + 8 q^{43} - 24 q^{44} - 2 q^{45} - 4 q^{46} + 8 q^{47} - 10 q^{49} - 2 q^{50} - 16 q^{51} - 24 q^{53} - 16 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 16 q^{58} + 12 q^{59} + 16 q^{60} + 16 q^{61} - 4 q^{63} - 28 q^{64} + 24 q^{66} - 4 q^{67} - 12 q^{68} + 4 q^{69} + 24 q^{70} + 4 q^{71} + 6 q^{72} - 24 q^{74} - 4 q^{76} + 32 q^{77} + 6 q^{80} + 10 q^{81} - 4 q^{82} + 24 q^{83} - 24 q^{84} - 4 q^{85} - 56 q^{86} - 16 q^{87} + 16 q^{88} + 12 q^{89} + 4 q^{90} + 16 q^{92} + 12 q^{93} - 12 q^{94} - 4 q^{95} - 8 q^{96} - 4 q^{97} - 42 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 - 16 * q^12 - 24 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 16 * q^21 + 8 * q^22 + 4 * q^24 + 4 * q^25 + 20 * q^28 - 4 * q^30 - 24 * q^31 + 6 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^40 - 12 * q^41 - 16 * q^42 + 8 * q^43 - 24 * q^44 - 2 * q^45 - 4 * q^46 + 8 * q^47 - 10 * q^49 - 2 * q^50 - 16 * q^51 - 24 * q^53 - 16 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 16 * q^58 + 12 * q^59 + 16 * q^60 + 16 * q^61 - 4 * q^63 - 28 * q^64 + 24 * q^66 - 4 * q^67 - 12 * q^68 + 4 * q^69 + 24 * q^70 + 4 * q^71 + 6 * q^72 - 24 * q^74 - 4 * q^76 + 32 * q^77 + 6 * q^80 + 10 * q^81 - 4 * q^82 + 24 * q^83 - 24 * q^84 - 4 * q^85 - 56 * q^86 - 16 * q^87 + 16 * q^88 + 12 * q^89 + 4 * q^90 + 16 * q^92 + 12 * q^93 - 12 * q^94 - 4 * q^95 - 8 * q^96 - 4 * q^97 - 42 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.207107	+	0.358719i	0.146447	+	0.253653i	0.929912	−	0.367783i	$-0.119883\pi$
$2$	0.207107	+	0.358719i	0.146447	+	0.253653i	−0.783465	+	0.621436i	$0.786550\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.292893	−	0.507306i	0.119573	−	0.207107i
$7$	−0.414214	+	0.717439i	−0.156558	+	0.271166i	−0.933625	−	0.358251i	$-0.883373\pi$
$7$	−0.414214	+	0.717439i	−0.156558	+	0.271166i	0.777067	+	0.629418i	$0.216706\pi$
$8$	1.58579			0.560660
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	0.292893	+	0.507306i	0.0883106	+	0.152958i	0.906797	−	0.421567i	$-0.138520\pi$
$11$	0.292893	+	0.507306i	0.0883106	+	0.152958i	−0.818487	+	0.574526i	$0.805187\pi$
$12$	−2.58579			−0.746452
$13$		0			0
$13$		0			0
$14$	−0.343146			−0.0917096
$15$	0.707107	+	1.22474i	0.182574	+	0.316228i
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	2.41421	−	4.18154i	0.585533	−	1.01417i	−0.409276	−	0.912411i	$-0.634219\pi$
$17$	2.41421	−	4.18154i	0.585533	−	1.01417i	0.994809	−	0.101762i	$-0.0324480\pi$
$18$	0.414214			0.0976311
$19$	1.70711	−	2.95680i	0.391637	−	0.678335i	−0.601028	−	0.799228i	$-0.705242\pi$
$19$	1.70711	−	2.95680i	0.391637	−	0.678335i	0.992666	+	0.120892i	$0.0385755\pi$
$20$	−0.914214	+	1.58346i	−0.204424	+	0.354073i
$21$	1.17157			0.255658
$22$	−0.121320	+	0.210133i	−0.0258656	+	0.0448005i
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	0.930281	−	0.366847i	$-0.119563\pi$
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	−0.782839	+	0.622224i	$0.786229\pi$
$24$	−1.12132	−	1.94218i	−0.228889	−	0.396447i
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.65685			−1.08866
$28$	0.757359	+	1.31178i	0.143127	+	0.247904i
$29$	−2.82843	−	4.89898i	−0.525226	−	0.909718i	−0.999568	−	0.0293774i	$-0.990648\pi$
$29$	−2.82843	−	4.89898i	−0.525226	−	0.909718i	0.474343	−	0.880340i	$-0.342686\pi$
$30$	−0.292893	+	0.507306i	−0.0534747	+	0.0926210i
$31$	−10.2426			−1.83963			−0.919816	−	0.392349i	$-0.871662\pi$
$31$	−10.2426			−1.83963			−0.919816	+	0.392349i	$0.871662\pi$
$32$	2.20711	−	3.82282i	0.390165	−	0.675786i
$33$	0.414214	−	0.717439i	0.0721053	−	0.124890i
$34$	2.00000			0.342997
$35$	0.414214	−	0.717439i	0.0700149	−	0.121269i
$36$	−0.914214	−	1.58346i	−0.152369	−	0.263911i
$37$	4.24264	+	7.34847i	0.697486	+	1.20808i	0.969335	+	0.245741i	$0.0790313\pi$
$37$	4.24264	+	7.34847i	0.697486	+	1.20808i	−0.271850	+	0.962340i	$0.587635\pi$
$38$	1.41421			0.229416
$39$		0			0
$40$	−1.58579			−0.250735
$41$	−4.41421	−	7.64564i	−0.689384	−	1.19405i	−0.972037	−	0.234826i	$-0.924548\pi$
$41$	−4.41421	−	7.64564i	−0.689384	−	1.19405i	0.282653	−	0.959222i	$-0.408786\pi$
$42$	0.242641	+	0.420266i	0.0374403	+	0.0648485i
$43$	−1.53553	+	2.65962i	−0.234167	+	0.405589i	−0.959030	−	0.283304i	$-0.908569\pi$
$43$	−1.53553	+	2.65962i	−0.234167	+	0.405589i	0.724863	+	0.688893i	$0.241903\pi$
$44$	1.07107			0.161470
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−0.292893	+	0.507306i	−0.0431847	+	0.0747982i
$47$	−0.828427			−0.120839			−0.0604193	−	0.998173i	$-0.519244\pi$
$47$	−0.828427			−0.120839			−0.0604193	+	0.998173i	$0.519244\pi$
$48$	−2.12132	+	3.67423i	−0.306186	+	0.530330i
$49$	3.15685	+	5.46783i	0.450979	+	0.781119i
$50$	0.207107	+	0.358719i	0.0292893	+	0.0507306i
$51$	−6.82843			−0.956171
$52$		0			0
$53$	−14.4853			−1.98971			−0.994853	−	0.101327i	$-0.967691\pi$
$53$	−14.4853			−1.98971			−0.994853	+	0.101327i	$0.967691\pi$
$54$	−1.17157	−	2.02922i	−0.159431	−	0.276142i
$55$	−0.292893	−	0.507306i	−0.0394937	−	0.0684051i
$56$	−0.656854	+	1.13770i	−0.0877758	+	0.152032i
$57$	−4.82843			−0.639541
$58$	1.17157	−	2.02922i	0.153835	−	0.266450i
$59$	5.12132	−	8.87039i	0.666739	−	1.15483i	−0.312072	−	0.950059i	$-0.601023\pi$
$59$	5.12132	−	8.87039i	0.666739	−	1.15483i	0.978811	−	0.204767i	$-0.0656438\pi$
$60$	2.58579			0.333824
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−2.12132	−	3.67423i	−0.269408	−	0.466628i
$63$	0.414214	+	0.717439i	0.0521860	+	0.0903888i
$64$	−4.17157			−0.521447
$65$		0			0
$66$	0.343146			0.0422383
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−4.41421	−	7.64564i	−0.535302	−	0.927170i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$	0.343146			0.0410138
$71$	−3.94975	+	6.84116i	−0.468749	+	0.811897i	−0.999362	−	0.0357174i	$-0.988628\pi$
$71$	−3.94975	+	6.84116i	−0.468749	+	0.811897i	0.530613	+	0.847614i	$0.321962\pi$
$72$	0.792893	−	1.37333i	0.0934434	−	0.161849i
$73$	8.48528			0.993127			0.496564	−	0.868000i	$-0.334595\pi$
$73$	8.48528			0.993127			0.496564	+	0.868000i	$0.334595\pi$
$74$	−1.75736	+	3.04384i	−0.204289	+	0.353839i
$75$	−0.707107	−	1.22474i	−0.0816497	−	0.141421i
$76$	−3.12132	−	5.40629i	−0.358040	−	0.620143i
$77$	−0.485281			−0.0553029
$78$		0			0
$79$	8.48528			0.954669			0.477334	−	0.878722i	$-0.341603\pi$
$79$	8.48528			0.954669			0.477334	+	0.878722i	$0.341603\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	1.82843	−	3.16693i	0.201916	−	0.349729i
$83$	8.82843			0.969046			0.484523	−	0.874779i	$-0.338993\pi$
$83$	8.82843			0.969046			0.484523	+	0.874779i	$0.338993\pi$
$84$	1.07107	−	1.85514i	0.116863	−	0.202413i
$85$	−2.41421	+	4.18154i	−0.261858	+	0.453552i
$86$	−1.27208			−0.137172
$87$	−4.00000	+	6.92820i	−0.428845	+	0.742781i
$88$	0.464466	+	0.804479i	0.0495123	+	0.0857577i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−0.414214			−0.0436619
$91$		0			0
$92$	2.58579			0.269587
$93$	7.24264	+	12.5446i	0.751027	+	1.30082i
$94$	−0.171573	−	0.297173i	−0.0176964	−	0.0306510i
$95$	−1.70711	+	2.95680i	−0.175145	+	0.303361i
$96$	−6.24264			−0.637137
$97$	1.82843	−	3.16693i	0.185649	−	0.321553i	−0.758146	−	0.652085i	$-0.773895\pi$
$97$	1.82843	−	3.16693i	0.185649	−	0.321553i	0.943795	+	0.330532i	$0.107228\pi$
$98$	−1.30761	+	2.26485i	−0.132089	+	0.228784i
$99$	0.585786			0.0588738
$100$	0.914214	−	1.58346i	0.0914214	−	0.158346i
$101$	−3.82843	−	6.63103i	−0.380943	−	0.659812i	0.610255	−	0.792205i	$-0.291067\pi$
$101$	−3.82843	−	6.63103i	−0.380943	−	0.659812i	−0.991197	+	0.132393i	$0.957734\pi$
$102$	−1.41421	−	2.44949i	−0.140028	−	0.242536i
$103$	17.4142			1.71587			0.857937	−	0.513755i	$-0.171746\pi$
$103$	17.4142			1.71587			0.857937	+	0.513755i	$0.171746\pi$
$104$		0			0
$105$	−1.17157			−0.114334
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	3.29289	+	5.70346i	0.318336	+	0.551374i	0.980141	−	0.198302i	$-0.0635426\pi$
$107$	3.29289	+	5.70346i	0.318336	+	0.551374i	−0.661805	+	0.749676i	$0.730209\pi$
$108$	−5.17157	+	8.95743i	−0.497635	+	0.861929i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	0.121320	−	0.210133i	0.0115674	−	0.0200354i
$111$	6.00000	−	10.3923i	0.569495	−	0.986394i
$112$	2.48528			0.234837
$113$	1.58579	−	2.74666i	0.149178	−	0.258384i	−0.781746	−	0.623597i	$-0.785671\pi$
$113$	1.58579	−	2.74666i	0.149178	−	0.258384i	0.930924	+	0.365213i	$0.119004\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−0.707107	−	1.22474i	−0.0659380	−	0.114208i
$116$	−10.3431			−0.960337
$117$		0			0
$118$	4.24264			0.390567
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$	1.12132	+	1.94218i	0.102362	+	0.177296i
$121$	5.32843	−	9.22911i	0.484402	−	0.839010i
$122$	3.31371			0.300009
$123$	−6.24264	+	10.8126i	−0.562880	+	0.974937i
$124$	−9.36396	+	16.2189i	−0.840909	+	1.45650i
$125$	−1.00000			−0.0894427
$126$	−0.171573	+	0.297173i	−0.0152849	+	0.0264743i
$127$	4.70711	+	8.15295i	0.417688	+	0.723457i	0.995706	−	0.0925666i	$-0.0295071\pi$
$127$	4.70711	+	8.15295i	0.417688	+	0.723457i	−0.578018	+	0.816024i	$0.696174\pi$
$128$	−5.27817	−	9.14207i	−0.466529	−	0.808052i
$129$	4.34315			0.382393
$130$		0			0
$131$	16.9706			1.48272			0.741362	−	0.671105i	$-0.234180\pi$
$131$	16.9706			1.48272			0.741362	+	0.671105i	$0.234180\pi$
$132$	−0.757359	−	1.31178i	−0.0659197	−	0.114176i
$133$	1.41421	+	2.44949i	0.122628	+	0.212398i
$134$	0.414214	−	0.717439i	0.0357826	−	0.0619773i
$135$	5.65685			0.486864
$136$	3.82843	−	6.63103i	0.328285	−	0.568606i
$137$	2.65685	−	4.60181i	0.226990	−	0.393159i	−0.729924	−	0.683528i	$-0.760445\pi$
$137$	2.65685	−	4.60181i	0.226990	−	0.393159i	0.956915	+	0.290369i	$0.0937781\pi$
$138$	0.828427			0.0705204
$139$	6.24264	−	10.8126i	0.529494	−	0.917110i	−0.469914	−	0.882712i	$-0.655715\pi$
$139$	6.24264	−	10.8126i	0.529494	−	0.917110i	0.999408	−	0.0343983i	$-0.0109515\pi$
$140$	−0.757359	−	1.31178i	−0.0640085	−	0.110866i
$141$	0.585786	+	1.01461i	0.0493321	+	0.0854457i
$142$	−3.27208			−0.274587
$143$		0			0
$144$	−3.00000			−0.250000
$145$	2.82843	+	4.89898i	0.234888	+	0.406838i
$146$	1.75736	+	3.04384i	0.145440	+	0.251910i
$147$	4.46447	−	7.73268i	0.368223	−	0.637781i
$148$	15.5147			1.27530
$149$	−0.171573	+	0.297173i	−0.0140558	+	0.0243454i	−0.872968	−	0.487778i	$-0.837808\pi$
$149$	−0.171573	+	0.297173i	−0.0140558	+	0.0243454i	0.858912	+	0.512123i	$0.171141\pi$
$150$	0.292893	−	0.507306i	0.0239146	−	0.0414214i
$151$	−18.2426			−1.48457			−0.742283	−	0.670087i	$-0.766257\pi$
$151$	−18.2426			−1.48457			−0.742283	+	0.670087i	$0.766257\pi$
$152$	2.70711	−	4.68885i	0.219575	−	0.380316i
$153$	−2.41421	−	4.18154i	−0.195178	−	0.338058i
$154$	−0.100505	−	0.174080i	−0.00809893	−	0.0140278i
$155$	10.2426			0.822709
$156$		0			0
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$	1.75736	+	3.04384i	0.139808	+	0.242155i
$159$	10.2426	+	17.7408i	0.812294	+	1.40693i
$160$	−2.20711	+	3.82282i	−0.174487	+	0.302221i
$161$	−1.17157			−0.0923329
$162$	−1.03553	+	1.79360i	−0.0813592	+	0.140918i
$163$	−7.48528	+	12.9649i	−0.586292	+	1.01549i	0.408420	+	0.912794i	$0.366080\pi$
$163$	−7.48528	+	12.9649i	−0.586292	+	1.01549i	−0.994713	+	0.102694i	$0.967254\pi$
$164$	−16.1421			−1.26049
$165$	−0.414214	+	0.717439i	−0.0322465	+	0.0558525i
$166$	1.82843	+	3.16693i	0.141913	+	0.245801i
$167$	−4.41421	−	7.64564i	−0.341582	−	0.591638i	0.643145	−	0.765745i	$-0.277629\pi$
$167$	−4.41421	−	7.64564i	−0.341582	−	0.591638i	−0.984727	+	0.174107i	$0.944296\pi$
$168$	1.85786			0.143337
$169$		0			0
$170$	−2.00000			−0.153393
$171$	−1.70711	−	2.95680i	−0.130546	−	0.226112i
$172$	2.80761	+	4.86293i	0.214078	+	0.370795i
$173$	−5.58579	+	9.67487i	−0.424679	+	0.735566i	−0.996390	−	0.0848887i	$-0.972947\pi$
$173$	−5.58579	+	9.67487i	−0.424679	+	0.735566i	0.571711	+	0.820455i	$0.306280\pi$
$174$	−3.31371			−0.251212
$175$	−0.414214	+	0.717439i	−0.0313116	+	0.0542333i
$176$	0.878680	−	1.52192i	0.0662330	−	0.114719i
$177$	−14.4853			−1.08878
$178$	−1.24264	+	2.15232i	−0.0931399	+	0.161323i
$179$	2.82843	+	4.89898i	0.211407	+	0.366167i	0.952155	−	0.305616i	$-0.0988623\pi$
$179$	2.82843	+	4.89898i	0.211407	+	0.366167i	−0.740748	+	0.671783i	$0.765529\pi$
$180$	0.914214	+	1.58346i	0.0681415	+	0.118024i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	−11.3137			−0.836333
$184$	1.12132	+	1.94218i	0.0826648	+	0.143180i
$185$	−4.24264	−	7.34847i	−0.311925	−	0.540270i
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	2.82843			0.206835
$188$	−0.757359	+	1.31178i	−0.0552361	+	0.0956717i
$189$	2.34315	−	4.05845i	0.170439	−	0.295209i
$190$	−1.41421			−0.102598
$191$	−6.82843	+	11.8272i	−0.494088	+	0.855785i	−0.999977	−	0.00681360i	$-0.997831\pi$
$191$	−6.82843	+	11.8272i	−0.494088	+	0.855785i	0.505889	+	0.862599i	$0.331164\pi$
$192$	2.94975	+	5.10911i	0.212880	+	0.368718i
$193$	7.82843	+	13.5592i	0.563503	+	0.976015i	0.997187	+	0.0749503i	$0.0238798\pi$
$193$	7.82843	+	13.5592i	0.563503	+	0.976015i	−0.433685	+	0.901065i	$0.642787\pi$
$194$	1.51472			0.108750
$195$		0			0
$196$	11.5442			0.824583
$197$	−11.4853	−	19.8931i	−0.818292	−	1.41732i	−0.906939	−	0.421261i	$-0.861588\pi$
$197$	−11.4853	−	19.8931i	−0.818292	−	1.41732i	0.0886471	−	0.996063i	$-0.471746\pi$
$198$	0.121320	+	0.210133i	0.00862186	+	0.0149335i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	1.58579			0.112132
$201$	−1.41421	+	2.44949i	−0.0997509	+	0.172774i
$202$	1.58579	−	2.74666i	0.111576	−	0.193255i
$203$	4.68629			0.328913
$204$	−6.24264	+	10.8126i	−0.437072	+	0.757031i
$205$	4.41421	+	7.64564i	0.308302	+	0.533995i
$206$	3.60660	+	6.24682i	0.251284	+	0.435236i
$207$	1.41421			0.0982946
$208$		0			0
$209$	2.00000			0.138343
$210$	−0.242641	−	0.420266i	−0.0167438	−	0.0290011i
$211$	9.65685	+	16.7262i	0.664805	+	1.15148i	0.979338	+	0.202230i	$0.0648188\pi$
$211$	9.65685	+	16.7262i	0.664805	+	1.15148i	−0.314533	+	0.949247i	$0.601848\pi$
$212$	−13.2426	+	22.9369i	−0.909508	+	1.57531i
$213$	11.1716			0.765464
$214$	−1.36396	+	2.36245i	−0.0932385	+	0.161494i
$215$	1.53553	−	2.65962i	0.104723	−	0.181385i
$216$	−8.97056			−0.610369
$217$	4.24264	−	7.34847i	0.288009	−	0.498847i
$218$	0.414214	+	0.717439i	0.0280541	+	0.0485911i
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$	−1.07107			−0.0722114
$221$		0			0
$222$	4.97056			0.333602
$223$	13.2426	+	22.9369i	0.886793	+	1.53597i	0.843645	+	0.536902i	$0.180405\pi$
$223$	13.2426	+	22.9369i	0.886793	+	1.53597i	0.0431479	+	0.999069i	$0.486261\pi$
$224$	1.82843	+	3.16693i	0.122167	+	0.211599i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	1.31371			0.0873866
$227$	−13.8284	+	23.9515i	−0.917825	+	1.58972i	−0.115113	+	0.993352i	$0.536723\pi$
$227$	−13.8284	+	23.9515i	−0.917825	+	1.58972i	−0.802712	+	0.596367i	$0.796610\pi$
$228$	−4.41421	+	7.64564i	−0.292338	+	0.506345i
$229$	−0.828427			−0.0547440			−0.0273720	−	0.999625i	$-0.508714\pi$
$229$	−0.828427			−0.0547440			−0.0273720	+	0.999625i	$0.508714\pi$
$230$	0.292893	−	0.507306i	0.0193128	−	0.0334508i
$231$	0.343146	+	0.594346i	0.0225773	+	0.0391051i
$232$	−4.48528	−	7.76874i	−0.294473	−	0.510042i
$233$	24.6274			1.61340			0.806698	−	0.590964i	$-0.201253\pi$
$233$	24.6274			1.61340			0.806698	+	0.590964i	$0.201253\pi$
$234$		0			0
$235$	0.828427			0.0540406
$236$	−9.36396	−	16.2189i	−0.609542	−	1.05576i
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$	−0.828427	+	1.43488i	−0.0536990	+	0.0930093i
$239$	0.585786			0.0378914			0.0189457	−	0.999821i	$-0.493969\pi$
$239$	0.585786			0.0378914			0.0189457	+	0.999821i	$0.493969\pi$
$240$	2.12132	−	3.67423i	0.136931	−	0.237171i
$241$	1.24264	−	2.15232i	0.0800455	−	0.138643i	−0.823224	−	0.567717i	$-0.807827\pi$
$241$	1.24264	−	2.15232i	0.0800455	−	0.138643i	0.903269	+	0.429074i	$0.141160\pi$
$242$	4.41421			0.283756
$243$	−4.94975	+	8.57321i	−0.317526	+	0.549972i
$244$	−7.31371	−	12.6677i	−0.468212	−	0.810967i
$245$	−3.15685	−	5.46783i	−0.201684	−	0.349327i
$246$	−5.17157			−0.329727
$247$		0			0
$248$	−16.2426			−1.03141
$249$	−6.24264	−	10.8126i	−0.395611	−	0.685219i
$250$	−0.207107	−	0.358719i	−0.0130986	−	0.0226874i
$251$	9.89949	−	17.1464i	0.624851	−	1.08227i	−0.363719	−	0.931509i	$-0.618493\pi$
$251$	9.89949	−	17.1464i	0.624851	−	1.08227i	0.988570	−	0.150764i	$-0.0481735\pi$
$252$	1.51472			0.0954183
$253$	−0.414214	+	0.717439i	−0.0260414	+	0.0451050i
$254$	−1.94975	+	3.37706i	−0.122338	+	0.211896i
$255$	6.82843			0.427613
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−8.17157	−	14.1536i	−0.509729	−	0.882876i	−0.999936	−	0.0112704i	$-0.996412\pi$
$257$	−8.17157	−	14.1536i	−0.509729	−	0.882876i	0.490208	−	0.871606i	$-0.336921\pi$
$258$	0.899495	+	1.55797i	0.0560001	+	0.0969950i
$259$	−7.02944			−0.436788
$260$		0			0
$261$	−5.65685			−0.350150
$262$	3.51472	+	6.08767i	0.217140	+	0.376098i
$263$	6.70711	+	11.6170i	0.413578	+	0.716338i	0.995278	−	0.0970654i	$-0.0309456\pi$
$263$	6.70711	+	11.6170i	0.413578	+	0.716338i	−0.581700	+	0.813403i	$0.697612\pi$
$264$	0.656854	−	1.13770i	0.0404266	−	0.0700209i
$265$	14.4853			0.889824
$266$	−0.585786	+	1.01461i	−0.0359169	+	0.0622098i
$267$	4.24264	−	7.34847i	0.259645	−	0.449719i
$268$	−3.65685			−0.223378
$269$	1.34315	−	2.32640i	0.0818930	−	0.141843i	−0.822170	−	0.569242i	$-0.807237\pi$
$269$	1.34315	−	2.32640i	0.0818930	−	0.141843i	0.904063	+	0.427399i	$0.140570\pi$
$270$	1.17157	+	2.02922i	0.0712997	+	0.123495i
$271$	0.636039	+	1.10165i	0.0386366	+	0.0669206i	0.884697	−	0.466166i	$-0.154365\pi$
$271$	0.636039	+	1.10165i	0.0386366	+	0.0669206i	−0.846060	+	0.533087i	$0.821032\pi$
$272$	−14.4853			−0.878299
$273$		0			0
$274$	2.20101			0.132968
$275$	0.292893	+	0.507306i	0.0176621	+	0.0305917i
$276$	−1.82843	−	3.16693i	−0.110058	−	0.190627i
$277$	3.58579	−	6.21076i	0.215449	−	0.373169i	−0.737962	−	0.674842i	$-0.764212\pi$
$277$	3.58579	−	6.21076i	0.215449	−	0.373169i	0.953411	+	0.301673i	$0.0975452\pi$
$278$	5.17157			0.310170
$279$	−5.12132	+	8.87039i	−0.306605	+	0.531056i
$280$	0.656854	−	1.13770i	0.0392545	−	0.0679909i
$281$	17.7990			1.06180			0.530899	−	0.847435i	$-0.321854\pi$
$281$	17.7990			1.06180			0.530899	+	0.847435i	$0.321854\pi$
$282$	−0.242641	+	0.420266i	−0.0144490	+	0.0250265i
$283$	−4.36396	−	7.55860i	−0.259411	−	0.449312i	0.706674	−	0.707540i	$-0.250195\pi$
$283$	−4.36396	−	7.55860i	−0.259411	−	0.449312i	−0.966084	+	0.258227i	$0.916862\pi$
$284$	7.22183	+	12.5086i	0.428536	+	0.742247i
$285$	4.82843			0.286011
$286$		0			0
$287$	7.31371			0.431715
$288$	−2.20711	−	3.82282i	−0.130055	−	0.225262i
$289$	−3.15685	−	5.46783i	−0.185697	−	0.321637i
$290$	−1.17157	+	2.02922i	−0.0687971	+	0.119160i
$291$	−5.17157			−0.303163
$292$	7.75736	−	13.4361i	0.453965	−	0.786291i
$293$	−1.07107	+	1.85514i	−0.0625724	+	0.108379i	−0.895615	−	0.444831i	$-0.853264\pi$
$293$	−1.07107	+	1.85514i	−0.0625724	+	0.108379i	0.833042	+	0.553210i	$0.186597\pi$
$294$	3.69848			0.215700
$295$	−5.12132	+	8.87039i	−0.298175	+	0.516454i
$296$	6.72792	+	11.6531i	0.391053	+	0.677323i
$297$	−1.65685	−	2.86976i	−0.0961404	−	0.166520i
$298$	−0.142136			−0.00823370
$299$		0			0
$300$	−2.58579			−0.149290
$301$	−1.27208	−	2.20330i	−0.0733214	−	0.126996i
$302$	−3.77817	−	6.54399i	−0.217410	−	0.376564i
$303$	−5.41421	+	9.37769i	−0.311038	+	0.538734i
$304$	−10.2426			−0.587456
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−19.1716			−1.09418			−0.547090	−	0.837074i	$-0.684264\pi$
$307$	−19.1716			−1.09418			−0.547090	+	0.837074i	$0.684264\pi$
$308$	−0.443651	+	0.768426i	−0.0252794	+	0.0437851i
$309$	−12.3137	−	21.3280i	−0.700502	−	1.21331i
$310$	2.12132	+	3.67423i	0.120483	+	0.208683i
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		0			0
$313$	0.828427			0.0468255			0.0234127	−	0.999726i	$-0.492547\pi$
$313$	0.828427			0.0468255			0.0234127	+	0.999726i	$0.492547\pi$
$314$	3.72792	+	6.45695i	0.210379	+	0.364387i
$315$	−0.414214	−	0.717439i	−0.0233383	−	0.0404231i
$316$	7.75736	−	13.4361i	0.436386	−	0.755842i
$317$	−26.1421			−1.46829			−0.734144	−	0.678993i	$-0.762416\pi$
$317$	−26.1421			−1.46829			−0.734144	+	0.678993i	$0.762416\pi$
$318$	−4.24264	+	7.34847i	−0.237915	+	0.412082i
$319$	1.65685	−	2.86976i	0.0927660	−	0.160675i
$320$	4.17157			0.233198
$321$	4.65685	−	8.06591i	0.259920	−	0.450195i
$322$	−0.242641	−	0.420266i	−0.0135218	−	0.0234205i
$323$	−8.24264	−	14.2767i	−0.458633	−	0.794375i
$324$	9.14214			0.507896
$325$		0			0
$326$	−6.20101			−0.343442
$327$	−1.41421	−	2.44949i	−0.0782062	−	0.135457i
$328$	−7.00000	−	12.1244i	−0.386510	−	0.669456i
$329$	0.343146	−	0.594346i	0.0189182	−	0.0327673i
$330$	−0.343146			−0.0188896
$331$	11.0208	−	19.0886i	0.605759	−	1.04921i	−0.386172	−	0.922427i	$-0.626203\pi$
$331$	11.0208	−	19.0886i	0.605759	−	1.04921i	0.991931	−	0.126778i	$-0.0404637\pi$
$332$	8.07107	−	13.9795i	0.442957	−	0.767225i
$333$	8.48528			0.464991
$334$	1.82843	−	3.16693i	0.100047	−	0.173287i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	−1.75736	−	3.04384i	−0.0958718	−	0.166055i
$337$	7.17157			0.390660			0.195330	−	0.980738i	$-0.437422\pi$
$337$	7.17157			0.390660			0.195330	+	0.980738i	$0.437422\pi$
$338$		0			0
$339$	−4.48528			−0.243607
$340$	4.41421	+	7.64564i	0.239394	+	0.414643i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	0.707107	−	1.22474i	0.0382360	−	0.0662266i
$343$	−11.0294			−0.595534
$344$	−2.43503	+	4.21759i	−0.131288	+	0.227397i
$345$	−1.00000	+	1.73205i	−0.0538382	+	0.0932505i
$346$	−4.62742			−0.248771
$347$	−2.12132	+	3.67423i	−0.113878	+	0.197243i	−0.917331	−	0.398126i	$-0.869661\pi$
$347$	−2.12132	+	3.67423i	−0.113878	+	0.197243i	0.803452	+	0.595369i	$0.202994\pi$
$348$	7.31371	+	12.6677i	0.392056	+	0.679061i
$349$	0.757359	+	1.31178i	0.0405405	+	0.0702182i	0.885584	−	0.464480i	$-0.153759\pi$
$349$	0.757359	+	1.31178i	0.0405405	+	0.0702182i	−0.845043	+	0.534698i	$0.820425\pi$
$350$	−0.343146			−0.0183419
$351$		0			0
$352$	2.58579			0.137823
$353$	4.58579	+	7.94282i	0.244077	+	0.422753i	0.961872	−	0.273501i	$-0.0881818\pi$
$353$	4.58579	+	7.94282i	0.244077	+	0.422753i	−0.717795	+	0.696255i	$0.754848\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	3.94975	−	6.84116i	0.209631	−	0.363091i
$356$	10.9706			0.581439
$357$	2.82843	−	4.89898i	0.149696	−	0.259281i
$358$	−1.17157	+	2.02922i	−0.0619196	+	0.107248i
$359$	27.8995			1.47248			0.736240	−	0.676721i	$-0.236600\pi$
$359$	27.8995			1.47248			0.736240	+	0.676721i	$0.236600\pi$
$360$	−0.792893	+	1.37333i	−0.0417891	+	0.0723809i
$361$	3.67157	+	6.35935i	0.193241	+	0.334703i
$362$		0			0
$363$	−15.0711			−0.791026
$364$		0			0
$365$	−8.48528			−0.444140
$366$	−2.34315	−	4.05845i	−0.122478	−	0.212138i
$367$	−2.22183	−	3.84831i	−0.115978	−	0.200880i	0.802192	−	0.597066i	$-0.203667\pi$
$367$	−2.22183	−	3.84831i	−0.115978	−	0.200880i	−0.918170	+	0.396186i	$0.870334\pi$
$368$	2.12132	−	3.67423i	0.110581	−	0.191533i
$369$	−8.82843			−0.459590
$370$	1.75736	−	3.04384i	0.0913608	−	0.158241i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$	26.4853			1.37320
$373$	12.6569	−	21.9223i	0.655347	−	1.13509i	−0.326460	−	0.945211i	$-0.605856\pi$
$373$	12.6569	−	21.9223i	0.655347	−	1.13509i	0.981807	−	0.189883i	$-0.0608110\pi$
$374$	0.585786	+	1.01461i	0.0302903	+	0.0524643i
$375$	0.707107	+	1.22474i	0.0365148	+	0.0632456i
$376$	−1.31371			−0.0677493
$377$		0			0
$378$	1.94113			0.0998407
$379$	7.46447	+	12.9288i	0.383424	+	0.664110i	0.991549	−	0.129731i	$-0.0414115\pi$
$379$	7.46447	+	12.9288i	0.383424	+	0.664110i	−0.608125	+	0.793841i	$0.708078\pi$
$380$	3.12132	+	5.40629i	0.160120	+	0.277337i
$381$	6.65685	−	11.5300i	0.341041	−	0.590700i
$382$	−5.65685			−0.289430
$383$	16.5563	−	28.6764i	0.845990	−	1.46530i	−0.0387688	−	0.999248i	$-0.512344\pi$
$383$	16.5563	−	28.6764i	0.845990	−	1.46530i	0.884759	−	0.466049i	$-0.154323\pi$
$384$	−7.46447	+	12.9288i	−0.380919	+	0.659772i
$385$	0.485281			0.0247322
$386$	−3.24264	+	5.61642i	−0.165046	+	0.285868i
$387$	1.53553	+	2.65962i	0.0780556	+	0.135196i
$388$	−3.34315	−	5.79050i	−0.169723	−	0.293968i
$389$	−16.6274			−0.843044			−0.421522	−	0.906818i	$-0.638504\pi$
$389$	−16.6274			−0.843044			−0.421522	+	0.906818i	$0.638504\pi$
$390$		0			0
$391$	6.82843			0.345328
$392$	5.00610	+	8.67081i	0.252846	+	0.437942i
$393$	−12.0000	−	20.7846i	−0.605320	−	1.04844i
$394$	4.75736	−	8.23999i	0.239672	−	0.415125i
$395$	−8.48528			−0.426941
$396$	0.535534	−	0.927572i	0.0269116	−	0.0466122i
$397$	−13.8995	+	24.0746i	−0.697596	+	1.20827i	0.271702	+	0.962381i	$0.412413\pi$
$397$	−13.8995	+	24.0746i	−0.697596	+	1.20827i	−0.969298	+	0.245890i	$0.920920\pi$
$398$	−1.65685			−0.0830506
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$	−1.50000	−	2.59808i	−0.0750000	−	0.129904i
$401$	8.65685	+	14.9941i	0.432303	+	0.748770i	0.997071	−	0.0764792i	$-0.0243679\pi$
$401$	8.65685	+	14.9941i	0.432303	+	0.748770i	−0.564769	+	0.825249i	$0.691035\pi$
$402$	−1.17157			−0.0584327
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−2.50000	−	4.33013i	−0.124226	−	0.215166i
$406$	0.970563	+	1.68106i	0.0481682	+	0.0834298i
$407$	−2.48528	+	4.30463i	−0.123191	+	0.213373i
$408$	−10.8284			−0.536087
$409$	6.41421	−	11.1097i	0.317162	−	0.549341i	−0.662732	−	0.748856i	$-0.730603\pi$
$409$	6.41421	−	11.1097i	0.317162	−	0.549341i	0.979895	+	0.199515i	$0.0639366\pi$
$410$	−1.82843	+	3.16693i	−0.0902996	+	0.156403i
$411$	−7.51472			−0.370674
$412$	15.9203	−	27.5748i	0.784337	−	1.35851i
$413$	4.24264	+	7.34847i	0.208767	+	0.361595i
$414$	0.292893	+	0.507306i	0.0143949	+	0.0249327i
$415$	−8.82843			−0.433370
$416$		0			0
$417$	−17.6569			−0.864660
$418$	0.414214	+	0.717439i	0.0202598	+	0.0350911i
$419$	−2.58579	−	4.47871i	−0.126324	−	0.218799i	0.795926	−	0.605394i	$-0.206985\pi$
$419$	−2.58579	−	4.47871i	−0.126324	−	0.218799i	−0.922250	+	0.386595i	$0.873651\pi$
$420$	−1.07107	+	1.85514i	−0.0522628	+	0.0905218i
$421$	1.02944			0.0501717			0.0250859	−	0.999685i	$-0.492014\pi$
$421$	1.02944			0.0501717			0.0250859	+	0.999685i	$0.492014\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	−0.414214	+	0.717439i	−0.0201398	+	0.0348831i
$424$	−22.9706			−1.11555
$425$	2.41421	−	4.18154i	0.117107	−	0.202835i
$426$	2.31371	+	4.00746i	0.112100	+	0.194162i
$427$	3.31371	+	5.73951i	0.160362	+	0.277754i
$428$	12.0416			0.582054
$429$		0			0
$430$	1.27208			0.0613450
$431$	1.80761	+	3.13088i	0.0870696	+	0.150809i	0.906271	−	0.422697i	$-0.138916\pi$
$431$	1.80761	+	3.13088i	0.0870696	+	0.150809i	−0.819202	+	0.573506i	$0.805583\pi$
$432$	8.48528	+	14.6969i	0.408248	+	0.707107i
$433$	1.82843	−	3.16693i	0.0878686	−	0.152193i	−0.818741	−	0.574162i	$-0.805328\pi$
$433$	1.82843	−	3.16693i	0.0878686	−	0.152193i	0.906610	+	0.421970i	$0.138661\pi$
$434$	3.51472			0.168712
$435$	4.00000	−	6.92820i	0.191785	−	0.332182i
$436$	1.82843	−	3.16693i	0.0875658	−	0.151668i
$437$	4.82843			0.230975
$438$	2.48528	−	4.30463i	0.118751	−	0.205683i
$439$	16.4853	+	28.5533i	0.786800	+	1.36278i	0.927918	+	0.372784i	$0.121597\pi$
$439$	16.4853	+	28.5533i	0.786800	+	1.36278i	−0.141119	+	0.989993i	$0.545070\pi$
$440$	−0.464466	−	0.804479i	−0.0221426	−	0.0383520i
$441$	6.31371			0.300653
$442$		0			0
$443$	−6.58579			−0.312900			−0.156450	−	0.987686i	$-0.550005\pi$
$443$	−6.58579			−0.312900			−0.156450	+	0.987686i	$0.550005\pi$
$444$	−10.9706	−	19.0016i	−0.520640	−	0.901775i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−5.48528	+	9.50079i	−0.259736	+	0.449875i
$447$	0.485281			0.0229530
$448$	1.72792	−	2.99285i	0.0816366	−	0.141399i
$449$	14.5563	−	25.2123i	0.686957	−	1.18984i	−0.285861	−	0.958271i	$-0.592280\pi$
$449$	14.5563	−	25.2123i	0.686957	−	1.18984i	0.972818	−	0.231573i	$-0.0743871\pi$
$450$	0.414214			0.0195262
$451$	2.58579	−	4.47871i	0.121760	−	0.210894i
$452$	−2.89949	−	5.02207i	−0.136381	−	0.236218i
$453$	12.8995	+	22.3426i	0.606071	+	1.04975i
$454$	−11.4558			−0.537649
$455$		0			0
$456$	−7.65685			−0.358565
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	0.575036	−	0.818128i	$-0.304988\pi$
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	−0.996038	+	0.0889312i	$0.971655\pi$
$458$	−0.171573	−	0.297173i	−0.00801707	−	0.0138860i
$459$	−13.6569	+	23.6544i	−0.637447	+	1.10409i
$460$	−2.58579			−0.120563
$461$	13.2426	−	22.9369i	0.616771	−	1.06828i	−0.373300	−	0.927711i	$-0.621774\pi$
$461$	13.2426	−	22.9369i	0.616771	−	1.06828i	0.990071	−	0.140568i	$-0.0448930\pi$
$462$	−0.142136	+	0.246186i	−0.00661275	+	0.0114536i
$463$	15.6569			0.727636			0.363818	−	0.931470i	$-0.381473\pi$
$463$	15.6569			0.727636			0.363818	+	0.931470i	$0.381473\pi$
$464$	−8.48528	+	14.6969i	−0.393919	+	0.682288i
$465$	−7.24264	−	12.5446i	−0.335869	−	0.581743i
$466$	5.10051	+	8.83433i	0.236276	+	0.409243i
$467$	−10.5858			−0.489852			−0.244926	−	0.969542i	$-0.578764\pi$
$467$	−10.5858			−0.489852			−0.244926	+	0.969542i	$0.578764\pi$
$468$		0			0
$469$	1.65685			0.0765064
$470$	0.171573	+	0.297173i	0.00791407	+	0.0137076i
$471$	−12.7279	−	22.0454i	−0.586472	−	1.01580i
$472$	8.12132	−	14.0665i	0.373814	−	0.647465i
$473$	−1.79899			−0.0827176
$474$	2.48528	−	4.30463i	0.114153	−	0.197718i
$475$	1.70711	−	2.95680i	0.0783274	−	0.135667i
$476$	7.31371			0.335223
$477$	−7.24264	+	12.5446i	−0.331618	+	0.574379i
$478$	0.121320	+	0.210133i	0.00554906	+	0.00961126i
$479$	−2.63604	−	4.56575i	−0.120444	−	0.208615i	0.799499	−	0.600667i	$-0.205098\pi$
$479$	−2.63604	−	4.56575i	−0.120444	−	0.208615i	−0.919943	+	0.392053i	$0.871765\pi$
$480$	6.24264			0.284936
$481$		0			0
$482$	1.02944			0.0468896
$483$	0.828427	+	1.43488i	0.0376947	+	0.0652892i
$484$	−9.74264	−	16.8747i	−0.442847	−	0.767034i
$485$	−1.82843	+	3.16693i	−0.0830246	+	0.143803i
$486$	−4.10051			−0.186003
$487$	11.4853	−	19.8931i	0.520448	−	0.901442i	−0.479270	−	0.877668i	$-0.659098\pi$
$487$	11.4853	−	19.8931i	0.520448	−	0.901442i	0.999717	−	0.0237742i	$-0.00756829\pi$
$488$	6.34315	−	10.9867i	0.287141	−	0.497342i
$489$	21.1716			0.957412
$490$	1.30761	−	2.26485i	0.0590719	−	0.102316i
$491$	−5.41421	−	9.37769i	−0.244340	−	0.423209i	0.717606	−	0.696449i	$-0.245238\pi$
$491$	−5.41421	−	9.37769i	−0.244340	−	0.423209i	−0.961946	+	0.273240i	$0.911905\pi$
$492$	11.4142	+	19.7700i	0.514592	+	0.891300i
$493$	−27.3137			−1.23015
$494$		0			0
$495$	−0.585786			−0.0263291
$496$	15.3640	+	26.6112i	0.689862	+	1.19488i
$497$	−3.27208	−	5.66741i	−0.146773	−	0.254218i
$498$	2.58579	−	4.47871i	0.115872	−	0.200696i
$499$	−10.4437			−0.467522			−0.233761	−	0.972294i	$-0.575103\pi$
$499$	−10.4437			−0.467522			−0.233761	+	0.972294i	$0.575103\pi$
$500$	−0.914214	+	1.58346i	−0.0408849	+	0.0708147i
$501$	−6.24264	+	10.8126i	−0.278901	+	0.483070i
$502$	8.20101			0.366029
$503$	−9.05025	+	15.6755i	−0.403531	+	0.698936i	−0.994149	−	0.108015i	$-0.965551\pi$
$503$	−9.05025	+	15.6755i	−0.403531	+	0.698936i	0.590618	+	0.806951i	$0.298884\pi$
$504$	0.656854	+	1.13770i	0.0292586	+	0.0506774i
$505$	3.82843	+	6.63103i	0.170363	+	0.295077i
$506$	−0.343146			−0.0152547
$507$		0			0
$508$	17.2132			0.763712
$509$	−10.5563	−	18.2841i	−0.467902	−	0.810430i	0.531425	−	0.847105i	$-0.321657\pi$
$509$	−10.5563	−	18.2841i	−0.467902	−	0.810430i	−0.999327	+	0.0366752i	$0.988323\pi$
$510$	1.41421	+	2.44949i	0.0626224	+	0.108465i
$511$	−3.51472	+	6.08767i	−0.155482	+	0.269303i
$512$	−22.7574			−1.00574
$513$	−9.65685	+	16.7262i	−0.426361	+	0.738478i
$514$	3.38478	−	5.86260i	0.149296	−	0.258588i
$515$	−17.4142			−0.767362
$516$	3.97056	−	6.87722i	0.174794	−	0.302753i
$517$	−0.242641	−	0.420266i	−0.0106713	−	0.0184833i
$518$	−1.45584	−	2.52160i	−0.0639661	−	0.110793i
$519$	15.7990			0.693499
$520$		0			0
$521$	−6.34315			−0.277898			−0.138949	−	0.990300i	$-0.544372\pi$
$521$	−6.34315			−0.277898			−0.138949	+	0.990300i	$0.544372\pi$
$522$	−1.17157	−	2.02922i	−0.0512784	−	0.0888167i
$523$	14.1213	+	24.4588i	0.617482	+	1.06951i	0.989944	+	0.141463i	$0.0451806\pi$
$523$	14.1213	+	24.4588i	0.617482	+	1.06951i	−0.372461	+	0.928048i	$0.621486\pi$
$524$	15.5147	−	26.8723i	0.677764	−	1.17392i
$525$	1.17157			0.0511316
$526$	−2.77817	+	4.81194i	−0.121134	+	0.209811i
$527$	−24.7279	+	42.8300i	−1.07717	+	1.86570i
$528$	−2.48528			−0.108158
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−5.12132	−	8.87039i	−0.222246	−	0.384942i
$532$	5.17157			0.224216
$533$		0			0
$534$	3.51472			0.152097
$535$	−3.29289	−	5.70346i	−0.142364	−	0.246582i
$536$	−1.58579	−	2.74666i	−0.0684955	−	0.118638i
$537$	4.00000	−	6.92820i	0.172613	−	0.298974i
$538$	1.11270			0.0479718
$539$	−1.84924	+	3.20298i	−0.0796525	+	0.137962i
$540$	5.17157	−	8.95743i	0.222549	−	0.385466i
$541$	12.8284			0.551537			0.275769	−	0.961224i	$-0.411068\pi$
$541$	12.8284			0.551537			0.275769	+	0.961224i	$0.411068\pi$
$542$	−0.263456	+	0.456319i	−0.0113164	+	0.0196006i
$543$		0			0
$544$	−10.6569	−	18.4582i	−0.456909	−	0.791389i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−29.2132			−1.24907			−0.624533	−	0.780998i	$-0.714711\pi$
$547$	−29.2132			−1.24907			−0.624533	+	0.780998i	$0.714711\pi$
$548$	−4.85786	−	8.41407i	−0.207518	−	0.359431i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	−0.121320	+	0.210133i	−0.00517312	+	0.00896010i
$551$	−19.3137			−0.822792
$552$	1.58579	−	2.74666i	0.0674956	−	0.116906i
$553$	−3.51472	+	6.08767i	−0.149461	+	0.258874i
$554$	2.97056			0.126207
$555$	−6.00000	+	10.3923i	−0.254686	+	0.441129i
$556$	−11.4142	−	19.7700i	−0.484070	−	0.838435i
$557$	1.89949	+	3.29002i	0.0804842	+	0.139403i	0.903458	−	0.428677i	$-0.141020\pi$
$557$	1.89949	+	3.29002i	0.0804842	+	0.139403i	−0.822974	+	0.568079i	$0.807687\pi$
$558$	−4.24264			−0.179605
$559$		0			0
$560$	−2.48528			−0.105022
$561$	−2.00000	−	3.46410i	−0.0844401	−	0.146254i
$562$	3.68629	+	6.38484i	0.155497	+	0.269328i
$563$	8.12132	−	14.0665i	0.342273	−	0.592834i	−0.642582	−	0.766217i	$-0.722137\pi$
$563$	8.12132	−	14.0665i	0.342273	−	0.592834i	0.984854	+	0.173383i	$0.0554700\pi$
$564$	2.14214			0.0902002
$565$	−1.58579	+	2.74666i	−0.0667145	+	0.115553i
$566$	1.80761	−	3.13088i	0.0759796	−	0.131601i
$567$	−4.14214			−0.173953
$568$	−6.26346	+	10.8486i	−0.262809	+	0.455198i
$569$	10.8284	+	18.7554i	0.453951	+	0.786267i	0.998627	−	0.0523799i	$-0.0166807\pi$
$569$	10.8284	+	18.7554i	0.453951	+	0.786267i	−0.544676	+	0.838647i	$0.683347\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	−28.4853			−1.19207			−0.596036	−	0.802958i	$-0.703258\pi$
$571$	−28.4853			−1.19207			−0.596036	+	0.802958i	$0.703258\pi$
$572$		0			0
$573$	19.3137			0.806842
$574$	1.51472	+	2.62357i	0.0632231	+	0.109506i
$575$	0.707107	+	1.22474i	0.0294884	+	0.0510754i
$576$	−2.08579	+	3.61269i	−0.0869078	+	0.150529i
$577$	29.1716			1.21443			0.607214	−	0.794538i	$-0.292287\pi$
$577$	29.1716			1.21443			0.607214	+	0.794538i	$0.292287\pi$
$578$	1.30761	−	2.26485i	0.0543895	−	0.0942053i
$579$	11.0711	−	19.1757i	0.460098	−	0.796913i
$580$	10.3431			0.429476
$581$	−3.65685	+	6.33386i	−0.151712	+	0.262773i
$582$	−1.07107	−	1.85514i	−0.0443972	−	0.0768982i
$583$	−4.24264	−	7.34847i	−0.175712	−	0.304342i
$584$	13.4558			0.556807
$585$		0			0
$586$	−0.887302			−0.0366541
$587$	15.8284	+	27.4156i	0.653309	+	1.13156i	0.982315	+	0.187237i	$0.0599531\pi$
$587$	15.8284	+	27.4156i	0.653309	+	1.13156i	−0.329006	+	0.944328i	$0.606714\pi$
$588$	−8.16295	−	14.1386i	−0.336634	−	0.583068i
$589$	−17.4853	+	30.2854i	−0.720468	+	1.24789i
$590$	−4.24264			−0.174667
$591$	−16.2426	+	28.1331i	−0.668133	+	1.15724i
$592$	12.7279	−	22.0454i	0.523114	−	0.906061i
$593$	−20.6274			−0.847066			−0.423533	−	0.905881i	$-0.639210\pi$
$593$	−20.6274			−0.847066			−0.423533	+	0.905881i	$0.639210\pi$
$594$	0.686292	−	1.18869i	0.0281589	−	0.0487726i
$595$	−2.00000	−	3.46410i	−0.0819920	−	0.142014i
$596$	0.313708	+	0.543359i	0.0128500	+	0.0222569i
$597$	5.65685			0.231520
$598$		0			0
$599$	−25.4558			−1.04010			−0.520049	−	0.854137i	$-0.674086\pi$
$599$	−25.4558			−1.04010			−0.520049	+	0.854137i	$0.674086\pi$
$600$	−1.12132	−	1.94218i	−0.0457777	−	0.0792893i
$601$	−0.313708	−	0.543359i	−0.0127964	−	0.0221641i	0.859556	−	0.511041i	$-0.170740\pi$
$601$	−0.313708	−	0.543359i	−0.0127964	−	0.0221641i	−0.872353	+	0.488877i	$0.837407\pi$
$602$	0.526912	−	0.912638i	0.0214753	−	0.0371964i
$603$	−2.00000			−0.0814463
$604$	−16.6777	+	28.8866i	−0.678605	+	1.17538i
$605$	−5.32843	+	9.22911i	−0.216631	+	0.375217i
$606$	−4.48528			−0.182202
$607$	−20.1213	+	34.8511i	−0.816699	+	1.41456i	0.0914022	+	0.995814i	$0.470865\pi$
$607$	−20.1213	+	34.8511i	−0.816699	+	1.41456i	−0.908101	+	0.418750i	$0.862468\pi$
$608$	−7.53553	−	13.0519i	−0.305606	−	0.529326i
$609$	−3.31371	−	5.73951i	−0.134278	−	0.232577i
$610$	−3.31371			−0.134168
$611$		0			0
$612$	−8.82843			−0.356868
$613$	−18.6569	−	32.3146i	−0.753543	−	1.30518i	−0.946095	−	0.323888i	$-0.895010\pi$
$613$	−18.6569	−	32.3146i	−0.753543	−	1.30518i	0.192552	−	0.981287i	$-0.438324\pi$
$614$	−3.97056	−	6.87722i	−0.160239	−	0.277542i
$615$	6.24264	−	10.8126i	0.251728	−	0.436005i
$616$	−0.769553			−0.0310062
$617$	−11.4853	+	19.8931i	−0.462380	+	0.800866i	−0.999079	−	0.0429081i	$-0.986338\pi$
$617$	−11.4853	+	19.8931i	−0.462380	+	0.800866i	0.536699	+	0.843774i	$0.319671\pi$
$618$	5.10051	−	8.83433i	0.205172	−	0.355369i
$619$	−10.2426			−0.411686			−0.205843	−	0.978585i	$-0.565994\pi$
$619$	−10.2426			−0.411686			−0.205843	+	0.978585i	$0.565994\pi$
$620$	9.36396	−	16.2189i	0.376066	−	0.651365i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	−1.75736	−	3.04384i	−0.0704637	−	0.122047i
$623$	−4.97056			−0.199141
$624$		0			0
$625$	1.00000			0.0400000
$626$	0.171573	+	0.297173i	0.00685743	+	0.0118774i
$627$	−1.41421	−	2.44949i	−0.0564782	−	0.0978232i
$628$	16.4558	−	28.5024i	0.656660	−	1.13737i
$629$	40.9706			1.63360
$630$	0.171573	−	0.297173i	0.00683563	−	0.0118397i
$631$	−9.12132	+	15.7986i	−0.363114	+	0.628932i	−0.988472	−	0.151406i	$-0.951620\pi$
$631$	−9.12132	+	15.7986i	−0.363114	+	0.628932i	0.625358	+	0.780338i	$0.284953\pi$
$632$	13.4558			0.535245
$633$	13.6569	−	23.6544i	0.542811	−	0.940177i
$634$	−5.41421	−	9.37769i	−0.215026	−	0.372436i
$635$	−4.70711	−	8.15295i	−0.186796	−	0.323540i
$636$	37.4558			1.48522
$637$		0			0
$638$	1.37258			0.0543411
$639$	3.94975	+	6.84116i	0.156250	+	0.270632i
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	−18.1716	+	31.4741i	−0.717734	+	1.24315i	0.244162	+	0.969735i	$0.421487\pi$
$641$	−18.1716	+	31.4741i	−0.717734	+	1.24315i	−0.961896	+	0.273417i	$0.911846\pi$
$642$	3.85786			0.152258
$643$	13.2426	−	22.9369i	0.522239	−	0.904544i	−0.477426	−	0.878672i	$-0.658430\pi$
$643$	13.2426	−	22.9369i	0.522239	−	0.904544i	0.999665	−	0.0258724i	$-0.00823635\pi$
$644$	−1.07107	+	1.85514i	−0.0422060	+	0.0731029i
$645$	−4.34315			−0.171011
$646$	3.41421	−	5.91359i	0.134330	−	0.232667i
$647$	−3.29289	−	5.70346i	−0.129457	−	0.224226i	0.794009	−	0.607906i	$-0.207990\pi$
$647$	−3.29289	−	5.70346i	−0.129457	−	0.224226i	−0.923466	+	0.383679i	$0.874657\pi$
$648$	3.96447	+	6.86666i	0.155739	+	0.269748i
$649$	6.00000			0.235521
$650$		0			0
$651$	−12.0000			−0.470317
$652$	13.6863	+	23.7054i	0.535997	+	0.928373i
$653$	−6.51472	−	11.2838i	−0.254941	−	0.441570i	0.709939	−	0.704263i	$-0.248723\pi$
$653$	−6.51472	−	11.2838i	−0.254941	−	0.441570i	−0.964879	+	0.262693i	$0.915389\pi$
$654$	0.585786	−	1.01461i	0.0229061	−	0.0396745i
$655$	−16.9706			−0.663095
$656$	−13.2426	+	22.9369i	−0.517038	+	0.895537i
$657$	4.24264	−	7.34847i	0.165521	−	0.286691i
$658$	0.284271			0.0110820
$659$	−23.0711	+	39.9603i	−0.898721	+	1.55663i	−0.0695907	+	0.997576i	$0.522169\pi$
$659$	−23.0711	+	39.9603i	−0.898721	+	1.55663i	−0.829130	+	0.559055i	$0.811164\pi$
$660$	0.757359	+	1.31178i	0.0294802	+	0.0510612i
$661$	−24.7990	−	42.9531i	−0.964569	−	1.67068i	−0.710769	−	0.703426i	$-0.751653\pi$
$661$	−24.7990	−	42.9531i	−0.964569	−	1.67068i	−0.253800	−	0.967257i	$-0.581681\pi$
$662$	9.12994			0.354845
$663$		0			0
$664$	14.0000			0.543305
$665$	−1.41421	−	2.44949i	−0.0548408	−	0.0949871i
$666$	1.75736	+	3.04384i	0.0680963	+	0.117946i
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−16.1421			−0.624558
$669$	18.7279	−	32.4377i	0.724063	−	1.25411i
$670$	−0.414214	+	0.717439i	−0.0160025	+	0.0277171i
$671$	4.68629			0.180912
$672$	2.58579	−	4.47871i	0.0997489	−	0.172770i
$673$	5.24264	+	9.08052i	0.202089	+	0.350028i	0.949201	−	0.314669i	$-0.101894\pi$
$673$	5.24264	+	9.08052i	0.202089	+	0.350028i	−0.747112	+	0.664698i	$0.768560\pi$
$674$	1.48528	+	2.57258i	0.0572109	+	0.0990922i
$675$	−5.65685			−0.217732
$676$		0			0
$677$	8.14214			0.312928			0.156464	−	0.987684i	$-0.449991\pi$
$677$	8.14214			0.312928			0.156464	+	0.987684i	$0.449991\pi$
$678$	−0.928932	−	1.60896i	−0.0356754	−	0.0617916i
$679$	1.51472	+	2.62357i	0.0581296	+	0.100683i
$680$	−3.82843	+	6.63103i	−0.146813	+	0.254288i
$681$	39.1127			1.49880
$682$	1.24264	−	2.15232i	0.0475832	−	0.0824165i
$683$	16.6569	−	28.8505i	0.637357	−	1.10393i	−0.348654	−	0.937252i	$-0.613361\pi$
$683$	16.6569	−	28.8505i	0.637357	−	1.10393i	0.986011	−	0.166683i	$-0.0533056\pi$
$684$	−6.24264			−0.238693
$685$	−2.65685	+	4.60181i	−0.101513	+	0.175826i
$686$	−2.28427	−	3.95647i	−0.0872139	−	0.151059i
$687$	0.585786	+	1.01461i	0.0223491	+	0.0387099i
$688$	9.21320			0.351250
$689$		0			0
$690$	−0.828427			−0.0315377
$691$	10.5355	+	18.2481i	0.400791	+	0.694190i	0.993822	−	0.110990i	$-0.0354022\pi$
$691$	10.5355	+	18.2481i	0.400791	+	0.694190i	−0.593031	+	0.805180i	$0.702069\pi$
$692$	10.2132	+	17.6898i	0.388248	+	0.672465i
$693$	−0.242641	+	0.420266i	−0.00921716	+	0.0159646i
$694$	−1.75736			−0.0667084
$695$	−6.24264	+	10.8126i	−0.236797	+	0.410144i
$696$	−6.34315	+	10.9867i	−0.240436	+	0.416448i
$697$	−42.6274			−1.61463
$698$	−0.313708	+	0.543359i	−0.0118740	+	0.0205664i
$699$	−17.4142	−	30.1623i	−0.658666	−	1.14084i
$700$	0.757359	+	1.31178i	0.0286255	+	0.0495808i
$701$	37.3137			1.40932			0.704660	−	0.709545i	$-0.251100\pi$
$701$	37.3137			1.40932			0.704660	+	0.709545i	$0.251100\pi$
$702$		0			0
$703$	28.9706			1.09265
$704$	−1.22183	−	2.11626i	−0.0460493	−	0.0797597i
$705$	−0.585786	−	1.01461i	−0.0220620	−	0.0382125i
$706$	−1.89949	+	3.29002i	−0.0714884	+	0.123822i
$707$	6.34315			0.238559
$708$	−13.2426	+	22.9369i	−0.497689	+	0.862022i
$709$	−8.55635	+	14.8200i	−0.321340	+	0.556578i	−0.980765	−	0.195193i	$-0.937467\pi$
$709$	−8.55635	+	14.8200i	−0.321340	+	0.556578i	0.659424	+	0.751771i	$0.270800\pi$
$710$	3.27208			0.122799
$711$	4.24264	−	7.34847i	0.159111	−	0.275589i
$712$	4.75736	+	8.23999i	0.178290	+	0.308807i
$713$	−7.24264	−	12.5446i	−0.271239	−	0.469800i
$714$	2.34315			0.0876900
$715$		0			0
$716$	10.3431			0.386542
$717$	−0.414214	−	0.717439i	−0.0154691	−	0.0267932i
$718$	5.77817	+	10.0081i	0.215640	+	0.373499i
$719$	2.48528	−	4.30463i	0.0926854	−	0.160536i	−0.815955	−	0.578116i	$-0.803788\pi$
$719$	2.48528	−	4.30463i	0.0926854	−	0.160536i	0.908640	+	0.417580i	$0.137122\pi$
$720$	3.00000			0.111803
$721$	−7.21320	+	12.4936i	−0.268634	+	0.465287i
$722$	−1.52082	+	2.63413i	−0.0565989	+	0.0980321i
$723$	−3.51472			−0.130714
$724$		0			0
$725$	−2.82843	−	4.89898i	−0.105045	−	0.181944i
$726$	−3.12132	−	5.40629i	−0.115843	−	0.200646i
$727$	19.3553			0.717850			0.358925	−	0.933366i	$-0.383143\pi$
$727$	19.3553			0.717850			0.358925	+	0.933366i	$0.383143\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−1.75736	−	3.04384i	−0.0650428	−	0.112657i
$731$	7.41421	+	12.8418i	0.274225	+	0.474971i
$732$	−10.3431	+	17.9149i	−0.382294	+	0.662152i
$733$	1.31371			0.0485229			0.0242615	−	0.999706i	$-0.492277\pi$
$733$	1.31371			0.0485229			0.0242615	+	0.999706i	$0.492277\pi$
$734$	0.920310	−	1.59402i	0.0339693	−	0.0588365i
$735$	−4.46447	+	7.73268i	−0.164674	+	0.285224i
$736$	6.24264			0.230107
$737$	0.585786	−	1.01461i	0.0215777	−	0.0373737i
$738$	−1.82843	−	3.16693i	−0.0673053	−	0.116576i
$739$	15.3640	+	26.6112i	0.565172	+	0.978907i	0.997034	+	0.0769673i	$0.0245237\pi$
$739$	15.3640	+	26.6112i	0.565172	+	0.978907i	−0.431861	+	0.901940i	$0.642143\pi$
$740$	−15.5147			−0.570332
$741$		0			0
$742$	4.97056			0.182475
$743$	−19.2426	−	33.3292i	−0.705944	−	1.22273i	−0.966350	−	0.257232i	$-0.917190\pi$
$743$	−19.2426	−	33.3292i	−0.705944	−	1.22273i	0.260406	−	0.965499i	$-0.416144\pi$
$744$	11.4853	+	19.8931i	0.421071	+	0.729316i
$745$	0.171573	−	0.297173i	0.00628594	−	0.0108876i
$746$	10.4853			0.383893
$747$	4.41421	−	7.64564i	0.161508	−	0.279739i
$748$	2.58579	−	4.47871i	0.0945457	−	0.163758i
$749$	−5.45584			−0.199352
$750$	−0.292893	+	0.507306i	−0.0106949	+	0.0185242i
$751$	22.2426	+	38.5254i	0.811645	+	1.40581i	0.911712	+	0.410830i	$0.134761\pi$
$751$	22.2426	+	38.5254i	0.811645	+	1.40581i	−0.100066	+	0.994981i	$0.531905\pi$
$752$	1.24264	+	2.15232i	0.0453144	+	0.0784869i
$753$	−28.0000			−1.02038
$754$		0			0
$755$	18.2426			0.663918
$756$	−4.28427	−	7.42058i	−0.155817	−	0.269884i
$757$	−2.07107	−	3.58719i	−0.0752742	−	0.130379i	0.825931	−	0.563771i	$-0.190650\pi$
$757$	−2.07107	−	3.58719i	−0.0752742	−	0.130379i	−0.901205	+	0.433392i	$0.857317\pi$
$758$	−3.09188	+	5.35530i	−0.112302	+	0.194513i
$759$	1.17157			0.0425254
$760$	−2.70711	+	4.68885i	−0.0981971	+	0.170082i
$761$	−18.3137	+	31.7203i	−0.663871	+	1.14986i	0.315719	+	0.948853i	$0.397754\pi$
$761$	−18.3137	+	31.7203i	−0.663871	+	1.14986i	−0.979590	+	0.201006i	$0.935579\pi$
$762$	5.51472			0.199777
$763$	−0.828427	+	1.43488i	−0.0299911	+	0.0519461i
$764$	12.4853	+	21.6251i	0.451702	+	0.782370i
$765$	2.41421	+	4.18154i	0.0872861	+	0.151184i
$766$	13.7157			0.495569
$767$		0			0
$768$	5.61522			0.202622
$769$	5.48528	+	9.50079i	0.197804	+	0.342607i	0.947816	−	0.318817i	$-0.103286\pi$
$769$	5.48528	+	9.50079i	0.197804	+	0.342607i	−0.750012	+	0.661424i	$0.769952\pi$
$770$	0.100505	+	0.174080i	0.00362195	+	0.00627340i
$771$	−11.5563	+	20.0162i	−0.416192	+	0.720865i
$772$	28.6274			1.03032
$773$	3.07107	−	5.31925i	0.110459	−	0.191320i	−0.805497	−	0.592600i	$-0.798101\pi$
$773$	3.07107	−	5.31925i	0.110459	−	0.191320i	0.915955	+	0.401280i	$0.131435\pi$
$774$	−0.636039	+	1.10165i	−0.0228619	+	0.0395981i
$775$	−10.2426			−0.367927
$776$	2.89949	−	5.02207i	0.104086	−	0.180282i
$777$	4.97056	+	8.60927i	0.178318	+	0.308856i
$778$	−3.44365	−	5.96458i	−0.123461	−	0.213840i
$779$	−30.1421			−1.07995
$780$		0			0
$781$	−4.62742			−0.165582
$782$	1.41421	+	2.44949i	0.0505722	+	0.0875936i
$783$	16.0000	+	27.7128i	0.571793	+	0.990375i
$784$	9.47056	−	16.4035i	0.338234	−	0.585839i
$785$	−18.0000			−0.642448
$786$	4.97056	−	8.60927i	0.177294	−	0.307082i
$787$	2.75736	−	4.77589i	0.0982892	−	0.170242i	−0.812687	−	0.582700i	$-0.801996\pi$
$787$	2.75736	−	4.77589i	0.0982892	−	0.170242i	0.910977	+	0.412458i	$0.135330\pi$
$788$	−42.0000			−1.49619
$789$	9.48528	−	16.4290i	0.337685	−	0.584888i
$790$	−1.75736	−	3.04384i	−0.0625240	−	0.108295i
$791$	1.31371	+	2.27541i	0.0467101	+	0.0809043i
$792$	0.928932			0.0330082
$793$		0			0
$794$	−11.5147			−0.408642
$795$	−10.2426	−	17.7408i	−0.363269	−	0.629200i
$796$	3.65685	+	6.33386i	0.129614	+	0.224498i
$797$	−5.48528	+	9.50079i	−0.194299	+	0.336535i	−0.946670	−	0.322204i	$-0.895576\pi$
$797$	−5.48528	+	9.50079i	−0.194299	+	0.336535i	0.752372	+	0.658739i	$0.228910\pi$
$798$	1.65685			0.0586520
$799$	−2.00000	+	3.46410i	−0.0707549	+	0.122551i
$800$	2.20711	−	3.82282i	0.0780330	−	0.135157i
$801$	6.00000			0.212000
$802$	−3.58579	+	6.21076i	−0.126619	+	0.219310i
$803$	2.48528	+	4.30463i	0.0877037	+	0.151907i
$804$	2.58579	+	4.47871i	0.0911937	+	0.157952i
$805$	1.17157			0.0412925
$806$		0			0
$807$	−3.79899			−0.133731
$808$	−6.07107	−	10.5154i	−0.213579	−	0.369930i
$809$	22.6274	+	39.1918i	0.795538	+	1.37791i	0.922497	+	0.386004i	$0.126145\pi$
$809$	22.6274	+	39.1918i	0.795538	+	1.37791i	−0.126960	+	0.991908i	$0.540522\pi$
$810$	1.03553	−	1.79360i	0.0363850	−	0.0630206i
$811$	−8.38478			−0.294429			−0.147215	−	0.989105i	$-0.547031\pi$
$811$	−8.38478			−0.294429			−0.147215	+	0.989105i	$0.547031\pi$
$812$	4.28427	−	7.42058i	0.150348	−	0.260411i
$813$	0.899495	−	1.55797i	0.0315467	−	0.0546404i
$814$	−2.05887			−0.0721635
$815$	7.48528	−	12.9649i	0.262198	−	0.454140i
$816$	10.2426	+	17.7408i	0.358564	+	0.621051i
$817$	5.24264	+	9.08052i	0.183417	+	0.317687i
$818$	5.31371			0.185789
$819$		0			0
$820$	16.1421			0.563708
$821$	19.6274	+	33.9957i	0.685002	+	1.18646i	0.973436	+	0.228958i	$0.0735318\pi$
$821$	19.6274	+	33.9957i	0.685002	+	1.18646i	−0.288435	+	0.957500i	$0.593135\pi$
$822$	−1.55635	−	2.69568i	−0.0542839	−	0.0940225i
$823$	−17.1924	+	29.7781i	−0.599289	+	1.03800i	0.393637	+	0.919266i	$0.371217\pi$
$823$	−17.1924	+	29.7781i	−0.599289	+	1.03800i	−0.992926	+	0.118733i	$0.962117\pi$
$824$	27.6152			0.962022
$825$	0.414214	−	0.717439i	0.0144211	−	0.0249780i
$826$	−1.75736	+	3.04384i	−0.0611464	+	0.105909i
$827$	−27.8579			−0.968713			−0.484356	−	0.874871i	$-0.660946\pi$
$827$	−27.8579			−0.968713			−0.484356	+	0.874871i	$0.660946\pi$
$828$	1.29289	−	2.23936i	0.0449311	−	0.0778230i
$829$	−3.51472	−	6.08767i	−0.122071	−	0.211434i	0.798513	−	0.601977i	$-0.205620\pi$
$829$	−3.51472	−	6.08767i	−0.122071	−	0.211434i	−0.920584	+	0.390544i	$0.872287\pi$
$830$	−1.82843	−	3.16693i	−0.0634656	−	0.109926i
$831$	−10.1421			−0.351827
$832$		0			0
$833$	30.4853			1.05625
$834$	−3.65685	−	6.33386i	−0.126627	−	0.219324i
$835$	4.41421	+	7.64564i	0.152760	+	0.264588i
$836$	1.82843	−	3.16693i	0.0632375	−	0.109531i
$837$	57.9411			2.00274
$838$	1.07107	−	1.85514i	0.0369994	−	0.0640849i
$839$	−9.36396	+	16.2189i	−0.323280	+	0.559937i	−0.981163	−	0.193183i	$-0.938119\pi$
$839$	−9.36396	+	16.2189i	−0.323280	+	0.559937i	0.657883	+	0.753120i	$0.271452\pi$
$840$	−1.85786			−0.0641024
$841$	−1.50000	+	2.59808i	−0.0517241	+	0.0895888i
$842$	0.213203	+	0.369279i	0.00734748	+	0.0127262i
$843$	−12.5858	−	21.7992i	−0.433478	−	0.750805i
$844$	35.3137			1.21555
$845$		0			0
$846$	−0.343146			−0.0117976
$847$	4.41421	+	7.64564i	0.151674	+	0.262707i
$848$	21.7279	+	37.6339i	0.746140	+	1.29235i
$849$	−6.17157	+	10.6895i	−0.211808	+	0.366862i
$850$	2.00000			0.0685994
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$	10.2132	−	17.6898i	0.349899	−	0.606042i
$853$	−37.4558			−1.28246			−0.641232	−	0.767347i	$-0.721576\pi$
$853$	−37.4558			−1.28246			−0.641232	+	0.767347i	$0.721576\pi$
$854$	−1.37258	+	2.37738i	−0.0469688	+	0.0813524i
$855$	1.70711	+	2.95680i	0.0583818	+	0.101120i
$856$	5.22183	+	9.04447i	0.178478	+	0.309134i
$857$	0.343146			0.0117216			0.00586082	−	0.999983i	$-0.498134\pi$
$857$	0.343146			0.0117216			0.00586082	+	0.999983i	$0.498134\pi$
$858$		0			0
$859$	11.7990			0.402576			0.201288	−	0.979532i	$-0.435487\pi$
$859$	11.7990			0.402576			0.201288	+	0.979532i	$0.435487\pi$
$860$	−2.80761	−	4.86293i	−0.0957388	−	0.165824i
$861$	−5.17157	−	8.95743i	−0.176247	−	0.305268i
$862$	−0.748737	+	1.29685i	−0.0255021	+	0.0441709i
$863$	−19.4558			−0.662285			−0.331142	−	0.943581i	$-0.607434\pi$
$863$	−19.4558			−0.662285			−0.331142	+	0.943581i	$0.607434\pi$
$864$	−12.4853	+	21.6251i	−0.424758	+	0.735702i
$865$	5.58579	−	9.67487i	0.189922	−	0.328955i
$866$	1.51472			0.0514722
$867$	−4.46447	+	7.73268i	−0.151621	+	0.262616i
$868$	−7.75736	−	13.4361i	−0.263302	−	0.456052i
$869$	2.48528	+	4.30463i	0.0843074	+	0.146025i
$870$	3.31371			0.112345
$871$		0			0
$872$	3.17157			0.107403
$873$	−1.82843	−	3.16693i	−0.0618829	−	0.107184i
$874$	1.00000	+	1.73205i	0.0338255	+	0.0585875i
$875$	0.414214	−	0.717439i	0.0140030	−	0.0242539i
$876$	−21.9411			−0.741322
$877$	1.34315	−	2.32640i	0.0453548	−	0.0785568i	−0.842457	−	0.538764i	$-0.818891\pi$
$877$	1.34315	−	2.32640i	0.0453548	−	0.0785568i	0.887812	+	0.460207i	$0.152225\pi$
$878$	−6.82843	+	11.8272i	−0.230448	+	0.399148i
$879$	3.02944			0.102180
$880$	−0.878680	+	1.52192i	−0.0296203	+	0.0513038i
$881$	−26.4853	−	45.8739i	−0.892312	−	1.54553i	−0.837097	−	0.547055i	$-0.815749\pi$
$881$	−26.4853	−	45.8739i	−0.892312	−	1.54553i	−0.0552151	−	0.998474i	$-0.517584\pi$
$882$	1.30761	+	2.26485i	0.0440296	+	0.0762615i
$883$	−32.2426			−1.08505			−0.542526	−	0.840039i	$-0.682532\pi$
$883$	−32.2426			−1.08505			−0.542526	+	0.840039i	$0.682532\pi$
$884$		0			0
$885$	14.4853			0.486917
$886$	−1.36396	−	2.36245i	−0.0458232	−	0.0793681i
$887$	−7.19239	−	12.4576i	−0.241497	−	0.418285i	0.719644	−	0.694343i	$-0.244305\pi$
$887$	−7.19239	−	12.4576i	−0.241497	−	0.418285i	−0.961141	+	0.276058i	$0.910972\pi$
$888$	9.51472	−	16.4800i	0.319293	−	0.553032i
$889$	−7.79899			−0.261570
$890$	1.24264	−	2.15232i	0.0416534	−	0.0721458i
$891$	−1.46447	+	2.53653i	−0.0490615	+	0.0849769i
$892$	48.4264			1.62144
$893$	−1.41421	+	2.44949i	−0.0473249	+	0.0819690i
$894$	0.100505	+	0.174080i	0.00336139	+	0.00582210i
$895$	−2.82843	−	4.89898i	−0.0945439	−	0.163755i
$896$	8.74517			0.292155
$897$		0			0
$898$	12.0589			0.402410
$899$	28.9706	+	50.1785i	0.966222	+	1.67355i
$900$	−0.914214	−	1.58346i	−0.0304738	−	0.0527821i
$901$	−34.9706	+	60.5708i	−1.16504	+	2.01791i
$902$	2.14214			0.0713253
$903$	−1.79899	+	3.11594i	−0.0598666	+	0.103692i
$904$	2.51472	−	4.35562i	0.0836383	−	0.144866i
$905$		0			0
$906$	−5.34315	+	9.25460i	−0.177514	+	0.307463i
$907$	16.6066	+	28.7635i	0.551413	+	0.955076i	0.998173	+	0.0604217i	$0.0192445\pi$
$907$	16.6066	+	28.7635i	0.551413	+	0.955076i	−0.446760	+	0.894654i	$0.647422\pi$
$908$	25.2843	+	43.7936i	0.839088	+	1.45334i
$909$	−7.65685			−0.253962
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	7.24264	+	12.5446i	0.239828	+	0.415394i
$913$	2.58579	+	4.47871i	0.0855770	+	0.148224i
$914$	3.72792	−	6.45695i	0.123309	−	0.213577i
$915$	11.3137			0.374020
$916$	−0.757359	+	1.31178i	−0.0250239	+	0.0433426i
$917$	−7.02944	+	12.1753i	−0.232132	+	0.402065i
$918$	−11.3137			−0.373408
$919$	8.24264	−	14.2767i	0.271900	−	0.470944i	−0.697449	−	0.716635i	$-0.745681\pi$
$919$	8.24264	−	14.2767i	0.271900	−	0.470944i	0.969348	+	0.245691i	$0.0790148\pi$
$920$	−1.12132	−	1.94218i	−0.0369688	−	0.0640319i
$921$	13.5563	+	23.4803i	0.446697	+	0.773702i
$922$	10.9706			0.361296
$923$		0			0
$924$	1.25483			0.0412810
$925$	4.24264	+	7.34847i	0.139497	+	0.241616i
$926$	3.24264	+	5.61642i	0.106560	+	0.184567i
$927$	8.70711	−	15.0812i	0.285979	−	0.495330i
$928$	−24.9706			−0.819699
$929$	5.58579	−	9.67487i	0.183264	−	0.317422i	−0.759726	−	0.650243i	$-0.774667\pi$
$929$	5.58579	−	9.67487i	0.183264	−	0.317422i	0.942990	+	0.332821i	$0.108000\pi$
$930$	3.00000	−	5.19615i	0.0983739	−	0.170389i
$931$	21.5563			0.706481
$932$	22.5147	−	38.9966i	0.737494	−	1.27738i
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$	−2.19239	−	3.79733i	−0.0717371	−	0.124252i
$935$	−2.82843			−0.0924995
$936$		0			0
$937$	10.9706			0.358393			0.179196	−	0.983813i	$-0.442650\pi$
$937$	10.9706			0.358393			0.179196	+	0.983813i	$0.442650\pi$
$938$	0.343146	+	0.594346i	0.0112041	+	0.0194061i
$939$	−0.585786	−	1.01461i	−0.0191164	−	0.0331106i
$940$	0.757359	−	1.31178i	0.0247023	−	0.0427857i
$941$	54.7696			1.78544			0.892718	−	0.450615i	$-0.148795\pi$
$941$	54.7696			1.78544			0.892718	+	0.450615i	$0.148795\pi$
$942$	5.27208	−	9.13151i	0.171774	−	0.297521i
$943$	6.24264	−	10.8126i	0.203288	−	0.352106i
$944$	−30.7279			−1.00011
$945$	−2.34315	+	4.05845i	−0.0762225	+	0.132021i
$946$	−0.372583	−	0.645333i	−0.0121137	−	0.0209816i
$947$	−22.5563	−	39.0687i	−0.732983	−	1.26956i	−0.955603	−	0.294658i	$-0.904794\pi$
$947$	−22.5563	−	39.0687i	−0.732983	−	1.26956i	0.222620	−	0.974905i	$-0.428539\pi$
$948$	−21.9411			−0.712615
$949$		0			0
$950$	1.41421			0.0458831
$951$	18.4853	+	32.0174i	0.599426	+	1.03824i
$952$	3.17157	+	5.49333i	0.102791	+	0.178040i
$953$	27.6274	−	47.8521i	0.894940	−	1.55008i	0.0610608	−	0.998134i	$-0.480552\pi$
$953$	27.6274	−	47.8521i	0.894940	−	1.55008i	0.833879	−	0.551947i	$-0.186115\pi$
$954$	−6.00000			−0.194257
$955$	6.82843	−	11.8272i	0.220963	−	0.382719i
$956$	0.535534	−	0.927572i	0.0173204	−	0.0299998i
$957$	−4.68629			−0.151486
$958$	1.09188	−	1.89120i	0.0352771	−	0.0611018i
$959$	2.20101	+	3.81226i	0.0710743	+	0.123104i
$960$	−2.94975	−	5.10911i	−0.0952027	−	0.164896i
$961$	73.9117			2.38425
$962$		0			0
$963$	6.58579			0.212224
$964$	−2.27208	−	3.93535i	−0.0731787	−	0.126749i
$965$	−7.82843	−	13.5592i	−0.252006	−	0.436487i
$966$	−0.343146	+	0.594346i	−0.0110405	+	0.0191228i
$967$	19.9411			0.641263			0.320632	−	0.947204i	$-0.396105\pi$
$967$	19.9411			0.641263			0.320632	+	0.947204i	$0.396105\pi$
$968$	8.44975	−	14.6354i	0.271585	−	0.470399i
$969$	−11.6569	+	20.1903i	−0.374472	+	0.648605i
$970$	−1.51472			−0.0486347
$971$	6.14214	−	10.6385i	0.197111	−	0.341405i	−0.750480	−	0.660893i	$-0.770178\pi$
$971$	6.14214	−	10.6385i	0.197111	−	0.341405i	0.947590	+	0.319488i	$0.103511\pi$
$972$	9.05025	+	15.6755i	0.290287	+	0.502792i
$973$	5.17157	+	8.95743i	0.165793	+	0.287162i
$974$	9.51472			0.304871
$975$		0			0
$976$	−24.0000			−0.768221
$977$	−28.2426	−	48.9177i	−0.903562	−	1.56502i	−0.822836	−	0.568279i	$-0.807609\pi$
$977$	−28.2426	−	48.9177i	−0.903562	−	1.56502i	−0.0807263	−	0.996736i	$-0.525724\pi$
$978$	4.38478	+	7.59466i	0.140210	+	0.242850i
$979$	−1.75736	+	3.04384i	−0.0561654	+	0.0972814i
$980$	−11.5442			−0.368765
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	2.24264	−	3.88437i	0.0715655	−	0.123955i
$983$	34.9706			1.11539			0.557694	−	0.830047i	$-0.311686\pi$
$983$	34.9706			1.11539			0.557694	+	0.830047i	$0.311686\pi$
$984$	−9.89949	+	17.1464i	−0.315584	+	0.546608i
$985$	11.4853	+	19.8931i	0.365951	+	0.633847i
$986$	−5.65685	−	9.79796i	−0.180151	−	0.312031i
$987$	−0.970563			−0.0308934
$988$		0			0
$989$	−4.34315			−0.138104
$990$	−0.121320	−	0.210133i	−0.00385581	−	0.00667847i
$991$	−7.51472	−	13.0159i	−0.238713	−	0.413463i	0.721632	−	0.692277i	$-0.243392\pi$
$991$	−7.51472	−	13.0159i	−0.238713	−	0.413463i	−0.960345	+	0.278814i	$0.910059\pi$
$992$	−22.6066	+	39.1558i	−0.717760	+	1.24320i
$993$	−31.1716			−0.989200
$994$	1.35534	−	2.34752i	0.0429887	−	0.0744587i
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$	−22.8284			−0.723346
$997$	−11.5858	+	20.0672i	−0.366926	+	0.635534i	−0.989083	−	0.147358i	$-0.952923\pi$
$997$	−11.5858	+	20.0672i	−0.366926	+	0.635534i	0.622158	+	0.782892i	$0.286256\pi$
$998$	−2.16295	−	3.74634i	−0.0684670	−	0.118588i
$999$	−24.0000	−	41.5692i	−0.759326	−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.c.146.2		4
13.2	odd	12		845.2.c.b.506.3		4
13.3	even	3		845.2.a.g.1.1		2
13.4	even	6		845.2.e.h.191.1		4
13.5	odd	4		845.2.m.f.361.3		8
13.6	odd	12		845.2.m.f.316.2		8
13.7	odd	12		845.2.m.f.316.3		8
13.8	odd	4		845.2.m.f.361.2		8
13.9	even	3	inner	845.2.e.c.191.2		4
13.10	even	6		65.2.a.b.1.2	✓	2
13.11	odd	12		845.2.c.b.506.2		4
13.12	even	2		845.2.e.h.146.1		4
39.23	odd	6		585.2.a.m.1.1		2
39.29	odd	6		7605.2.a.x.1.2		2
52.23	odd	6		1040.2.a.j.1.1		2
65.23	odd	12		325.2.b.f.274.2		4
65.29	even	6		4225.2.a.r.1.2		2
65.49	even	6		325.2.a.i.1.1		2
65.62	odd	12		325.2.b.f.274.3		4
91.62	odd	6		3185.2.a.j.1.2		2
104.75	odd	6		4160.2.a.z.1.2		2
104.101	even	6		4160.2.a.bf.1.1		2
143.10	odd	6		7865.2.a.j.1.1		2
156.23	even	6		9360.2.a.cd.1.2		2
195.23	even	12		2925.2.c.r.2224.3		4
195.62	even	12		2925.2.c.r.2224.2		4
195.179	odd	6		2925.2.a.u.1.2		2
260.179	odd	6		5200.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.b.1.2	✓	2	13.10	even	6
325.2.a.i.1.1		2	65.49	even	6
325.2.b.f.274.2		4	65.23	odd	12
325.2.b.f.274.3		4	65.62	odd	12
585.2.a.m.1.1		2	39.23	odd	6
845.2.a.g.1.1		2	13.3	even	3
845.2.c.b.506.2		4	13.11	odd	12
845.2.c.b.506.3		4	13.2	odd	12
845.2.e.c.146.2		4	1.1	even	1	trivial
845.2.e.c.191.2		4	13.9	even	3	inner
845.2.e.h.146.1		4	13.12	even	2
845.2.e.h.191.1		4	13.4	even	6
845.2.m.f.316.2		8	13.6	odd	12
845.2.m.f.316.3		8	13.7	odd	12
845.2.m.f.361.2		8	13.8	odd	4
845.2.m.f.361.3		8	13.5	odd	4
1040.2.a.j.1.1		2	52.23	odd	6
2925.2.a.u.1.2		2	195.179	odd	6
2925.2.c.r.2224.2		4	195.62	even	12
2925.2.c.r.2224.3		4	195.23	even	12
3185.2.a.j.1.2		2	91.62	odd	6
4160.2.a.z.1.2		2	104.75	odd	6
4160.2.a.bf.1.1		2	104.101	even	6
4225.2.a.r.1.2		2	65.29	even	6
5200.2.a.bu.1.2		2	260.179	odd	6
7605.2.a.x.1.2		2	39.29	odd	6
7865.2.a.j.1.1		2	143.10	odd	6
9360.2.a.cd.1.2		2	156.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.00000 q^{5} +(0.292893 - 0.507306i) q^{6} +(-0.414214 + 0.717439i) q^{7} +1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.207107 + 0.358719i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(0.914214 - 1.58346i) q^{4} -1.00000 q^{5} +(0.292893 - 0.507306i) q^{6} +(-0.414214 + 0.717439i) q^{7} +1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(0.292893 + 0.507306i) q^{11} -2.58579 q^{12} -0.343146 q^{14} +(0.707107 + 1.22474i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.41421 - 4.18154i) q^{17} +0.414214 q^{18} +(1.70711 - 2.95680i) q^{19} +(-0.914214 + 1.58346i) q^{20} +1.17157 q^{21} +(-0.121320 + 0.210133i) q^{22} +(0.707107 + 1.22474i) q^{23} +(-1.12132 - 1.94218i) q^{24} +1.00000 q^{25} -5.65685 q^{27} +(0.757359 + 1.31178i) q^{28} +(-2.82843 - 4.89898i) q^{29} +(-0.292893 + 0.507306i) q^{30} -10.2426 q^{31} +(2.20711 - 3.82282i) q^{32} +(0.414214 - 0.717439i) q^{33} +2.00000 q^{34} +(0.414214 - 0.717439i) q^{35} +(-0.914214 - 1.58346i) q^{36} +(4.24264 + 7.34847i) q^{37} +1.41421 q^{38} -1.58579 q^{40} +(-4.41421 - 7.64564i) q^{41} +(0.242641 + 0.420266i) q^{42} +(-1.53553 + 2.65962i) q^{43} +1.07107 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.292893 + 0.507306i) q^{46} -0.828427 q^{47} +(-2.12132 + 3.67423i) q^{48} +(3.15685 + 5.46783i) q^{49} +(0.207107 + 0.358719i) q^{50} -6.82843 q^{51} -14.4853 q^{53} +(-1.17157 - 2.02922i) q^{54} +(-0.292893 - 0.507306i) q^{55} +(-0.656854 + 1.13770i) q^{56} -4.82843 q^{57} +(1.17157 - 2.02922i) q^{58} +(5.12132 - 8.87039i) q^{59} +2.58579 q^{60} +(4.00000 - 6.92820i) q^{61} +(-2.12132 - 3.67423i) q^{62} +(0.414214 + 0.717439i) q^{63} -4.17157 q^{64} +0.343146 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-4.41421 - 7.64564i) q^{68} +(1.00000 - 1.73205i) q^{69} +0.343146 q^{70} +(-3.94975 + 6.84116i) q^{71} +(0.792893 - 1.37333i) q^{72} +8.48528 q^{73} +(-1.75736 + 3.04384i) q^{74} +(-0.707107 - 1.22474i) q^{75} +(-3.12132 - 5.40629i) q^{76} -0.485281 q^{77} +8.48528 q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.82843 - 3.16693i) q^{82} +8.82843 q^{83} +(1.07107 - 1.85514i) q^{84} +(-2.41421 + 4.18154i) q^{85} -1.27208 q^{86} +(-4.00000 + 6.92820i) q^{87} +(0.464466 + 0.804479i) q^{88} +(3.00000 + 5.19615i) q^{89} -0.414214 q^{90} +2.58579 q^{92} +(7.24264 + 12.5446i) q^{93} +(-0.171573 - 0.297173i) q^{94} +(-1.70711 + 2.95680i) q^{95} -6.24264 q^{96} +(1.82843 - 3.16693i) q^{97} +(-1.30761 + 2.26485i) q^{98} +0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} - 16 q^{12} - 24 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 16 q^{21} + 8 q^{22} + 4 q^{24} + 4 q^{25} + 20 q^{28} - 4 q^{30} - 24 q^{31} + 6 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{40} - 12 q^{41} - 16 q^{42} + 8 q^{43} - 24 q^{44} - 2 q^{45} - 4 q^{46} + 8 q^{47} - 10 q^{49} - 2 q^{50} - 16 q^{51} - 24 q^{53} - 16 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 16 q^{58} + 12 q^{59} + 16 q^{60} + 16 q^{61} - 4 q^{63} - 28 q^{64} + 24 q^{66} - 4 q^{67} - 12 q^{68} + 4 q^{69} + 24 q^{70} + 4 q^{71} + 6 q^{72} - 24 q^{74} - 4 q^{76} + 32 q^{77} + 6 q^{80} + 10 q^{81} - 4 q^{82} + 24 q^{83} - 24 q^{84} - 4 q^{85} - 56 q^{86} - 16 q^{87} + 16 q^{88} + 12 q^{89} + 4 q^{90} + 16 q^{92} + 12 q^{93} - 12 q^{94} - 4 q^{95} - 8 q^{96} - 4 q^{97} - 42 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 - 16 * q^12 - 24 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 16 * q^21 + 8 * q^22 + 4 * q^24 + 4 * q^25 + 20 * q^28 - 4 * q^30 - 24 * q^31 + 6 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^40 - 12 * q^41 - 16 * q^42 + 8 * q^43 - 24 * q^44 - 2 * q^45 - 4 * q^46 + 8 * q^47 - 10 * q^49 - 2 * q^50 - 16 * q^51 - 24 * q^53 - 16 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 16 * q^58 + 12 * q^59 + 16 * q^60 + 16 * q^61 - 4 * q^63 - 28 * q^64 + 24 * q^66 - 4 * q^67 - 12 * q^68 + 4 * q^69 + 24 * q^70 + 4 * q^71 + 6 * q^72 - 24 * q^74 - 4 * q^76 + 32 * q^77 + 6 * q^80 + 10 * q^81 - 4 * q^82 + 24 * q^83 - 24 * q^84 - 4 * q^85 - 56 * q^86 - 16 * q^87 + 16 * q^88 + 12 * q^89 + 4 * q^90 + 16 * q^92 + 12 * q^93 - 12 * q^94 - 4 * q^95 - 8 * q^96 - 4 * q^97 - 42 * q^98 + 8 * q^99

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